In Welsh, Ireland is called 'Iwerddon' (13 c. 'Ywerdon', 14 c. 'Iwerdon'). Seen here in Branwen ferch Llŷr from the Red Book of Hergest:

Ac ual yd oedynt yn eisted yuelly, wynt a welynt teir llong ar dec, yn dyuot o deheu Iwerdon...

And as they sat thus, they beheld thirteen ships coming from the south of Ireland...

In early Irish, Britain is called 'Alba' (though the implicit meaning is the north of Britain, ie. Caledonia). Seen here in Táin Bó Cúalnge from the Book of the Dun Cow:

‘Cia do chomainm-siu?’ ol Medb frisin n-ingin. ‘Fedelm banfili do Chonnachtaib mo ainm-sea,’ or ind ingen. ‘Can dothéig?’ or Medb. ‘A h-Albain iar foglaim filidechta,’ or ind ingen.

‘What is your name,’ asked Medb of the maiden. ‘I am Feidelm, the poetess of Connacht,’ said the maiden. ‘Whence do you come?’ asked Medb. ‘From Albion after learning the art of divination,’ answered the maiden.

The distinctions may be more explicit in later texts. Seen here in a different recension of Táin Bó Cúalnge from the Book of Leinster, which distinguishes the Gaels, Britons and Saxons:

Dáig dámbad ésin tísad and, ticfaitis slúaig ⁊ sochaide ⁊ forgla fer nHérend filet maróen ris, ⁊ giada betis fora chind i n-óenbaile ⁊ n-óendáil ⁊ i n-óentochim ⁊ i n-óenlongphurt ⁊ i n-óentulaig fir Hérend ⁊ Alban, Bretain ⁊ Saxain...

There is nothing that he would not pledge for his honour's sake. For if it were he who had come, armies and hosts and the pick of the men of Ireland who are with him would have come too, and even though the men of Ireland and the men of Scotland, the Britons and the Saxons...